Lagrangian reduction of generalized nonholonomic systems

HERNÁN CENDRA; SEBASTIÁN J. FERRARO; SERGIO GRILLO

JOURNAL OF GEOMETRY AND PHYSICS

Año: 2008 vol. 58 p. 1271 - 1290

0393-0440

In this paper we study the Lagrangian reduction of generalized nonholonomic systems (GNHS) with symmetry. We restrict ourselves to those GNHS, defined on a configuration space Q, with kinematic constraints given by a general submanifold C_K subset TQ , and variational constraints given by a distribution C_V on Q. We develop a reduction  procedure that is similar to that for nonholonomic systems satisfying d’Alembert’s principle, i.e. with C_K a distribution and C_V = C_K . Special care is taken in identifying the geometrical  structures and mappings involved. We illustrate the general theory with an example.